The three-time grand slam champion experienced difficulties when dropping a set in a previous round against another wildcard, Marco Chiudinelli, and Zverev broke Wawrinka six times in winning 6-2 5-7 6-1.
It was the first time in six years the German had recorded a victory over a top-10 ranked opponent and his reward, as well as a spot in next week's Paris Masters main draw, is a semi-final meeting with Marin Cilic, who defeated Marcel Granollers 6-3 6-3.
The highest seed remaining in the tournament is Kei Nishikori as he claimed his 55th win on the tour this year, and his first ever over Juan Martin del Potro.
The Argentinian had not dropped a set to Nishikori in their previous four meetings but the world No.5 claimed a solitary break in either set to advance courtesy of a 7-5 6-4 victory.
"I saved a lot of important points with my serve," said Nishikori, who had 10 break chances and took one in each set.
"I played good tactics today."
Nishikori is seeking a second title of the season.
In Saturday's semi-final, Nishikori plays Gilles Muller of Luxembourg, who earlier outlasted Federico Delbonis of Argentina 6-7 (7-4) 6-4 7-6 (7-3).
